I believe it is true the changes were mostly cosmetic. The Model 8 had a straight grip, the Model 81, a pistol grip. Also, the .300 Savage, which appeared around 1920 or 21 I think, was offered in the Model 81. It was not available in the Model 8. The Model 8 probably commands more money, since it was a John Browning design and the first successful semi-auto sporting rifle. He patented the design in 1900. Being a Browning design, it is built like a tank and I think most any one you find will function well. I have a Model 81 in .300 Savage and I have shot it many times. Being a long-recoil semi-auto, the whole barrel assembly recoils in order to open the bolt and cycle the action. The bolt lugs lock in an extension of the barrel rather than in receiver mortises. The receiver, which therefore does not have to withstand the pressure of the round, is of thin metal. This is a workable design which has since been used in more modern arms. I think the current Browning Sporting BAR, and maybe the LAR, use this locking method.
My gun functions well and is fairly accurate, but it certainly won't shame any bolt action rifles. It likes to toss the very hot empties straight up and back on my nose. The original butt plate is steel, and though you may not think of the .300 Savage as being a heavy recoil number, the Model 81 thumps you real good. If you intend to hunt, the Model 81 in .300 Savage would be far superior to a Model 8 in .30 Remington, which has ballistics comparable to the .30-30 Win.